Final answer:
Using the conservation of momentum, the velocity of the bullet before it hits the wood is calculated to be 8.9918 m/s, which is closest to option d, 8.2 m/s in the given choices.
Step-by-step explanation:
The question pertains to the concept of conservation of momentum in physics, which states that the total momentum of a closed system remains constant if no external forces act on it. In the scenario where a bullet sticks to a block of wood, we can use the formula for conservation of momentum:
p_initial = p_final
Where:
- p_initial is the momentum of the bullet before the collision,
- p_final is the momentum of the combined bullet and block after the collision.
Since the wood is initially at rest, its momentum is 0. The momentum of the bullet is the product of its mass and velocity, and the final momentum is the product of the total mass (bullet and wood) and their shared velocity. By equating the initial and final momenta and solving for the bullet's velocity, we can find the answer.
The mass of the bullet is 24.4 kg, the mass of the wood is 25.7 kg, and the velocity of the block (and the bullet inside it) after collision is 4.4 m/s. Using the conservation of momentum:
(mass of bullet) * (velocity of bullet) = (total mass) * (velocity after collision)
24.4 kg * velocity of bullet = (24.4 kg + 25.7 kg) * 4.4 m/s
Solving for velocity of bullet gives:
velocity of bullet = (50.1 kg * 4.4 m/s) / 24.4 kg = 8.9918 m/s
Therefore, the closest answer to this calculated velocity is 9.0 m/s, which is not listed among the options, suggesting there might be a typo in the mass values or a rounding error. For the provided options, the closest one is 8.2 m/s (option d).